The GCC offered a deal that gives embattled President Ali Abdullah Saleh immunity if he stands down. Saleh, who has faced mounting opposition at least since the beginning of the year, has balked on the measure.
Meanwhile, scores are left dead across the country as security forces clash with demonstrators. The GCC in a statement said it is time to move ahead with the deal.
"The council urged the all parties in Yemen to sign the agreement, which is the best way out of the crisis and spare the country further political division and deterioration of security," a GCC statement was quoted by al-Arabiya as saying.
Yasin Said Numan, a former Yemeni prime minister and secretary-general of the opposition Socialist Party, said in a Tuesday interview with Bloomberg News the country was facing a collapse unless the GCC plan was implemented.
He said the people in the streets are refusing any delay, warning there would be "catastrophic consequences" without a deal to end Saleh's tenure.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Kate Middleton recycles dress at movie premiere